The following workaround works only in Linux version of the game. The game uses an older version of SDL2 which lacks the support for DualShock 4.

32 Bit library of SDL2 package needs to be installed.

Replace older SDL 2 library included with the game

Open lib32 folder located in the game's directory.

Rename libSDL2-2.0.so.0 into something else as a backup.

Open the Terminal through file manager's Open Current Directory In Terminal option and type in:

ln -s /usr/lib32/libSDL2-2.0.so ./libSDL2-2.0.so.0

The game will now use the SDL2 library from your system which was installed through the package manager which is much more recent. Alternatively you can compile SDL2 itself (do not forget to instruct to make a 32 bit version of it) and use that instead.